Polar and Rectangular Coordinates Interactive Applet

① This interactive applet demonstrates the relationship between polar coordinates (r, α) and rectangular coordinates (x, y) for a point in the plane, allowing users to see how the same location is represented in both systems. ② Core mathematical concepts include polar and Cartesian coordinate definitions, angle measurement, coordinate axes, and the conversion formulas between the two systems. ③ Construction details: The applet uses GeoGebra commands such as OrthogonalLine to create perpendicular lines, Intersect to find intersection points, Segment to draw line segments, Point to mark key points, Angle to display the polar angle, and Textfield/InputBox for user input. Objects include A, f, B, b, C, c, D, α, r, e, g, xa, ya, and multiple text labels, all linked dynamically. ④ Suitable for high school or early college students learning analytic geometry or introductory calculus, and useful for classroom demonstrations or self-study to build intuition about coordinate transformations.